Arrange pita wedges in a single layer on a baking sheet. Lightly brush pita wedges with 2 tablespoons oil; bake at 350° for 20 minutes or until golden.
Combine 1 cup water and bulgur in a large bowl. Let stand 30 minutes or until bulgur is tender. Drain bulgur through a fine sieve; discard liquid. Place bulgur in a medium bowl. Add remaining 2 tablespoons oil, tomato, parsley, onion, mint, juice, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and red pepper; toss well. Refrigerate for 30 minutes.
Bring a medium saucepan of water to a boil. With a slotted spoon, carefully lower eggs into pan; cook 6 minutes. Drain and rinse eggs with cold running water until cool (about 1 minute). Peel eggs. Place 1/3 cup tabbouleh and 4 pita wedges on each of 6 plates; top each serving with 1 egg. Sprinkle eggs with remaining 1/4 teaspoon salt and 1/4 teaspoon black pepper.
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Good, solid tabbouleh. I've had better but this was simpler than most. I loved the soft-boiled egg on top. The runny yolk was a great added sauce. I served this with a side of baba ghanoush and pita wedges. The portion was really small though.